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Unformatted text preview: Chapter 07 - Capital Asset Pricing and Arbitrage Pricing Theory CHAPTER 07 CAPITAL ASSET PRICING AND ARBITRAGE PRICING THEORY 1. The required rate of return on a stock is related to the required rate of return on the stock market via beta. Assuming the beta of Google remains constant, the increase in the risk of the market will increase the required rate of return on the market, and thus increase the required rate of return on Google. 2. An example of this scenario would be an investment in the SMB and HML. As of yet, there are no vehicles (index funds or ETFs) to directly invest in SMB and HML. While they may prove superior to the single index model, they are not yet practical, even for professional investors. 3. The APT may exist without the CAPM, but not the other way. Thus, statement a is possible, but not b. The reason being, that the APT accepts the principle of risk and return, which is central to CAPM, without making any assumptions regarding individual investors and their portfolios. These assumptions are necessary to CAPM. 4. E(r P ) = r f + β [E(r M ) – r f ] 20% = 5% + β (15% – 5%) ⇒ β = 15/10 = 1.5 5. If the beta of the security doubles, then so will its risk premium. The current risk premium for the stock is: (13% - 7%) = 6%, so the new risk premium would be 12%, and the new discount rate for the security would be: 12% + 7% = 19% If the stock pays a constant dividend in perpetuity, then we know from the original data that the dividend (D) must satisfy the equation for a perpetuity: Price = Dividend/Discount rate 40 = D/0.13 ⇒ D = 40 × 0.13 = $5.20 At the new discount rate of 19%, the stock would be worth: $5.20/0.19 = $27.37 The increase in stock risk has lowered the value of the stock by 31.58%. 6. The cash flows for the project comprise a 10-year annuity of $10 million per year plus an additional payment in the tenth year of $10 million (so that the total payment in the tenth year is $20 million). The appropriate discount rate for the project is: r f + β [E(r M ) – r f ] = 9% + 1.7(19% – 9%) = 26% Using this discount rate: NPV = –20 + + ∑ = 10 1 t t 26 . 1 10 10 26 . 1 10 7-1 Chapter 07 - Capital Asset Pricing and Arbitrage Pricing Theory = –20 + [10 × Annuity factor (26%, 10 years)] + [10 × PV factor (26%, 10 years)] = 15.64 The internal rate of return on the project is 49.55%. The highest value that beta can take before the hurdle rate exceeds the IRR is determined by: 49.55% = 9% + β (19% – 9%) ⇒ β = 40.55/10 = 4.055 7. a. False. β = 0 implies E(r) = r f , not zero. b. False. Investors require a risk premium for bearing systematic (i.e., market or undiversifiable) risk. c. False. You should invest 0.75 of your portfolio in the market portfolio, and the remainder in T-bills. Then: β P = (0.75 × 1) + (0.25 × 0) = 0.75 8....
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